Let a and b be two unit vectors.

Question

Let $\hat a$ and $\hat b$ be two unit vectors. If the vectors $\vec c=\hat a+2\hat b$ and $\vec d=5\hat a-4\hat b$ are perpendicular to each other, then the angle between $\hat a$ and $\hat b$ is:

Accepted Answer

$\vec c\cdot\vec d=0$: $(\hat a+2\hat b)\cdot(5\hat a-4\hat b)=5-8+6\hat a\cdot\hat b=0 \implies \hat a\cdot\hat b=\dfrac12 \implies 	heta=\dfrac\pi3$

Solutions · 1